Signaling system utilizing



@do @www ml SIGNALING SYSTEM UTILIZING AS SIGNALING CHANNELS THE MNOR TRANSMITTING BANDS OF A LOADED LINE v Filed July 9, 1924 3 Sheets-Shee 1 y a mm1 mi 10M .ngi mmf mil) Ich m ma www1 IFP. S. HOYT SIGNALNG SYSTEM UTILIZING AS SIGNALING CHANNELS THE MINOR TRANSMITTING BANDS OF A LOADED LINE ATTORNEY c. E2 W25., lm

E5. HUYT SIGNALING SYSTEM UTILXZNG AS SIGNALING CHANNELS THE MINOR TRANSMITTING BANDS OF A LOADED LINE Filed July 9, 1924 3 Sheets-Sheet 3 ATTORNEY Piatented ct. 12, 1926.

-O'T, 0F RIVER EDGE, NE E JERSEY, ASSEGIJOR TO AMERCAN V'JljL32.EONE

AND TELEGt-AEH CGMPANY, A CGRIFOBATLLN OF NEVI YORK.

SXGNALING SYSTEM: UTLZING AS SGNALING' CHRNNELS MNOB TRANS- lvITTING BANBS GF .la LOADED LINE.

Application filed July 9,

to be utilized as channels 'for signaling purposes (including any communication purposes or any operating purposes)in addition to utilization of the major or principal 'transmitting band.

Another object is to provide a loaded line having` transmitting` bands of any desired locations and Widths-not incompatible with inherent relations (set 'forth in due place in this specification).

(Throughout these specilications and claims the term line7 used in a generic sense to include cables7 as Well as open- Wire lines. The loading ot the line may be Wholly lumped, as in loading coils; or it may be in part lumped, and in part distributed smoothly or nniitormly, as by surrounding each line-Wire with a material of high inagnetic permeability-such as perm alloy, tor example.)

For the better understanding of the abjects ot my invention, certain preliminary remarks will be made regarding the minor transmitting bands, together With the major or principal transmitting bant z lt ivelldfnoivn, in the art, that a loaded line without any distributed inductance would have only one transmitting band and only one attenuating band; the former eX- tending trom Zero frequency to the so-called critical frequency, and the latter from the critical frequency to infinite frequenciesthe critical frequency being the name given to the sharply defined transition lre quency between the transmitting band and the attenuating band ot the corresponding non-dissipative loaded line. Actually, hovvever, every line-even a cable-*has some distributed inductance. l3nt it is not generally lniovvn that the presence oit distributed inductance in any loaded line whose loading is at least partly lumped introduces into the aforesaid attenuating band an inlinite number ot transmitting bands. rthese additional transmitting' bands, which usu l* are relatively narrow and located at tively Wide intervals, are herein termed the niinor7 transmitting bands to distinguish them trom the major7 or principal transmitting band-the name herein given Serial Nc. 725,081.

to the Well-known relatively Wide transmitting band ot any loaded line (the first or lowest transu'iitting band). Since every natural line has some distributed inductaaee et its own, all et the bands are present when the loading is Wholly lumped, as Well as When the loading is partly lumped and partly distributed smoothly.

Since a smooth line has a transmitting band extending from zero to infinite trequcncies, an alternative statement is that the application ot lumped loading to a smooth line introduces into this preexisting transmitting band an iniinite number of attenta ating bands.

its a result oit a thorough-going theoretical study l have deduced general mathe-.

matinal formulas by means of which the locations and widths of the minor transmitting bands can be calculated in the case et any given loaded line; or by means ot which a loaded line can be so designed that its minoi` transmitting bands Will have any preassigned locations and Widths-not incompatilgile with inherent relations. I am thus enabled to attain the aforesaid objects ol .my invention.

lviy invention may now be more fullyv understood by means ot the following descriptionl when read in connection with the accomjjianying drawings, of which Figure l represents schematically one end ot a loaded line provided with signaling apparatus to enable several of the minor transmitting bands to be utilized, by means of carrier currents, as signaling channels-in addition to utilization ot the major transmitting band 'for ordinary telephonie and telegraphic purposes. 2 represents merely the loaded line itself, together Wit-h the mathematical syn'xbols employed in this speciiication for denoting the electrical constants thereof. Fig. 8 is a scale illustrating the relative locations and Widths of the transmitting bands and attenuating bands ot a loaded line, the quantity D being proportional to the frequency. The heavily-drawn segments represent transmitting bands; the lightly dravfn segmen s, attenuating bands. Fig. t is a set ot mathematical curves which l have provided in order to facilitate determining the locations ot the transmitting bands of any given loaded line; and, on the other hand, to tacilitate the designing ot a loaded line tohavefspecitied locationsof its transmitting bands. Fig. 5 is a curve showing the locations and Widths of the btransmitting andthe att-enuating bands of a specific loaded linechosen for illustrative purposes. The humps in the curve correspond to attenuatiiigbands, and the-valleys between correspond to transmitting bands or channels.

Xt will be recalled that the first. mentioned;

object of my invention is to Vprovide appropriate signaling apparatus in combinationvviithiany loaded/line to enable-its minor transmittingbands (besi'des'rits major transmit/'ting bandztofbe utilized as channelsY for` signaling purposes. Fig. l illustrates hovvy this.- object can be attained. It represents one-endort'such-aisystem; theother end, notshown, would be similarror approximately. similar, f connecting the two vends is a. loaded line,v only a smallv portion of which is shoivniinililig.I 1S. The arrangement inuFig, lf' isl such' to enable the utilizationl of sixv minorl bands-two for telegraph transmittin-g; ltavoi forvtelegraph receiving., one for telephone transmitting,v and one for telephone' receiving-inaddition to utiliza- .tionf of the major transmitting band for' ordinaryf telephone and teregiaplr purposes. The modulators, detectors, andiampliiiers-showin may be of'an-y ot the Wellknownl types usedi inf carrier` telephony and! telegraphyg' tlie-lters-maybe of the Camp- Y belltypea Although'in-eXi-sting loaded lines none ofther minor transmitting bands is Wide enoughi toA servev as atel'ephone channel, yetit 1s possible, b'yso designing/thef loaded.`

line as to have a i'elatively'large ratio of distributed inductancef to coi-l? inductance (for instance, by application .ofisinoothloadingiii the form -of- 'permailloy, for eXainpl'e)'fr to render one or-more ofthe minor 4bands tostate the precise meanings ofthe terms:

attenuatingf' transmitting b`and andb`an l: Infthe limiting case of no dissipation a: line having lumped loading, in addition tosmoothly distributedv inductance, would have sharply demarcated 'frequency-ranges of Zefroattenuation, and' other frequencyranges of non-zero attenuationthe former termed* transmitting bands, andthe latter attenuating bands. But no actual. line is entirely non-dissipative; and the presence of, dissipation introduces some attenuation into the transmitting bands androunds out their sharp corners, thus somewhat obscur` ing` the transition `frequencies. Hence for an actual dissipativeloaded-Yy line the transition frequencies, and therewith the transmitting and the attenuating bands, .are defined as vmeaning" those: ofthe corresponding. nondissipative loaded line. That is, if A denotes the attenuation .constant (real` component of the propagation constant EIA-MB):

of 'thef corresponding; non-dissipativef loaded line, thenthe transmittinggbands areldeiinedi to be the frequency-ranges in- Which A20,"

andi. the: attenuating bands the firequencyeranges lin-which1i-7f0s This inode of definition is-siinilar to the..V

Vfamiliar procedure adoptedi in detining'the critical frequency"7 of a iloaded line asnieaning the critical'i frequency' that the same linei Would'lhave if non-dissipative. (1Thecritical :frequenc-y isthe usuallyI employediy term for the transition frequency constituting the upper boundary point. ofthe only transmitt'iiig band usually recognized-namely, the.- iirst or lowest transmitting band, herein termed theinajor transmitting bandp).r

The salient facts and formulas pertaininwtothe locations oflthe transmittingbands;

(and the intermediate attenuating bands);

will next-be presented; but, toy avoid digressions, the derivations ofl the formulas Will!` be deferred to the latter partfofthe specificationjust preceding'the claims.

The fundainentall mathematical'. symbols.-

pertaining to the loaded. line have the meaningsindi'catedin Fig. 2: SA denotes the spac the inducing of the loading coils, and tance ofi each loading coil. L1 and C, denote the1 smoothly orv uniformly distributed line-inductance and'y line-capacity per uniti length, soy thatLsL1 andl SG1 are the indue-- tance andcaqjiacityl of each line-seginent be-I tween loadingfcoils. y denotesthe ration of line-segmenti inductance sLl to loading' coil-'I iiiductanfce Lf', that is,

AzsLl/Ii. ('11)y f' `denotes the frequency; isA already remarked, the smoothly disitrib'uted inductance lil ina-y consist'Y partlyof artiiicial'- smoothv` loading, in addition ytol the naturalvinductlance L11 of the line itself:

Thel general features pertainingto the 10.-- cations and? Widthsoftlife transmitting and? the a-t'teiiu'ating bands of a loadedr linev are representedon they D-scarlein Fig. 3; D is proportioiial'to the frequency, and( hasy the value delined byl the equation D @fsa/LE #rfa/anso@ (2)` As represented by F ig. 3, a loaded line has an iniinite sequence oi alternate transmittinga-nd attenuating loa-nds,.beginningv with a transmit-ting band. (The 'transmitting bands are drawn heavy, the attenuate in@` bands light.) The lirst transmittino,v band is the one thatV is herein termed the major or principal transmitting' band because .it is much wider thaA any of the succeeding` transn'iitting;v bands and is the band regularly utilized lor signaling' purposes. The remaining` tiansmittinp, bands are the ones herein termed the minor transmittinp` bands.

llt is convenient to employ the term conn pound band to denote the band consisting ot' a transmitting;l band and the siicceeding attenuatina,l band. For any speciic loaded line, the widths ot all the compound bands are equal; though the transmitting; bandsbecome continually narrower with increasing -frequency, and the attentiating bands become continually wider-while their sum is constant. The D-width oit each com` pound band has the simple value Tr/.

ln 1T ig. 3, the compound bands are numw bered 1, 2, 3, n, Thus, DI1 denotes the transition value ot D within the nth compound band; that is, Dn is the value of D at the transition point between the nth transmittingh band and the nth attenuating baud. Diam denotes the transition value ot D between the (tt-nth and ath compound bands; and hence denotes the transition value ot D between the (n-Il)tl1 attenuatinn; band and the nth transmitting' band. Thus Duim and Dn are respectively the lowvalid for 71:2, 3, 4, but not for 01:1. For the case ot a:1, so that DH:D1, the

rllhe smaller a, the more convergent are these lorn'iulas. Formula (11) is highly convergent, even when a is as large as unity or even considerably larger. Formula (10) is much less convergent than (11) but is satist'actorily convergent when a is a small traction: or. stated more generally, when a/tll, is small. in the next paragraph is given a widely applicable formula ot successive approximation for Dn valid for all the values ot a including 01:1, and suitable even 'tor large values ot ilfith D-cZ- denoted by Tm a formula ot successive approximation tor rn is w2er/i4 u n el seo 5040 604800 119750400 er and upper boundary points of the nth transmitting band. m

vWith regard to the ath compound band it will be noted that there are two kinds ot transition points-namely the internal transition point D11, and the external or boundary points DIH,n and DWH.

The D-width ot each compound band being- 1r/2, the boundary points ot the ath compound band have the simple values D11-1in: (7/L-l)7T/Qa DlwwrnW/Z; and hence, by (2), the corresponding bound* ary frequencies have the values fx1-1,11: (77- 1)/281/1101;

fn,n+1=7l/231./L1C1 (6) The location oit the internal transition point Dn of D within the nth compound band has no such simple formula as have the external or boundary points D 1,n and DMN; tor Dn is a root ot a transcendental equation, namely,

and hence Dn can be expressed only in an in- Finite series ot terms or ot operations. 1n particular (for 72:1),

l)1 tan D1:/\. (8) With DML denoted7 for brevity, by duY so a power series formula for DD is i an (i. 4 3) t) a a) a) 56 23 a 6 actual t appropriate power-series formula is proximate value T n in terms of Tn and the known quantities )t and dn. 7, in turn, may be used in the formula in order to calculate a still more accurate approximate value Tmn; and so on, until the last computed value of Tn agrees as closely as necessary with the computed value ust preceding it. Ott cours-e, the more accurate is the approximate value constituted by TQ, the fewer will be the applications of (l2) necessary to compute 7 to the required accuracy. First approximation values ttor 7 are represented by the formulas:

a i T ,1: Fil-1- 5) when a1, (13) as can b seen from formulas (10) and (11) respectively; lWhen 'riz-1,. rn-:131, since fdl-:O:

A-notherformula of successiveapproximation for Tn is T :tan- 1% (125) l n 'r'u bruti not convergent' for will unless A isv very small' By means ofthe preceding formulas (10) (l1), (l2), (l5), L have computed the curves, in Fig.. 4, of

'nEDn Dri-1m as function of'a wit'hwas-parameter, cov ering a widerange of )t and thefirst eight values of n'. Since the value of Dn is immediately obtainable valid for all the values: of n, that is, fon In particular, the critical'. frequency f, (namely, the lowest transition.l

Wzl, 2, 3,

frequency, that is, the frequency constituting the upper boundary point ofthe first or-` inajor transmitting band) has the value f1:fD1/7l'8'\/L1C1. I If f, den-etes the value of f1 in the limiting case of no distributed-inductance (1L1.:0,1.

so that A20), then ffies/@ es by (17), (l), and (11) for ('11) shows that' approaches l when )t approaches O.

As` already stated, the mathematical proofs of the formulas and statements hereinbefore set down will be furnished in. the latter part of this specifica-tion, preceding the claims.

The foregoing formulas and graphs enable thelocations and widths of the transmitting bands of any loaded line to be computed; and, on the other hand, enable a loaded line to be so designed as to have transmitting bands of preassigned locations and; widths-so tartas-compatible with inherentl relations.

maria-ing the` inherent. relations jiist re-l ferred to.

@ne inherent.relation-represented inv Fig,

S-has' already been brought out, namely that the Widths of all the compoundbands are equal; hence that the distances'between thel lower edges ofI allY transmitting bands are equal.

Another inherentfrelation-a'lso represented! in Fig. Bie-is that the transifnitti ngy bandsr grow narrowen and narrowerf withA increasing frequencywhence thel attenuating. bandslgrow wider andrwider. y l

ri`he external or boundary'- transition fre.

quencies fn 1, andl fumi, of. the ritlrcom-I pou-ndA band (any compound band) depend on only one parameterFnainely,the product 8.2141501. The

azLlCl parametersfnainely the product and the ratio EsLl/l.

Thus, fixingLlG, fixes allof.. the external transition frequencies Afixing.

SQLIC'I an'dlXE-Slil/L fires all of the transitionl frequencies-ex.- ternaland internal. Fixiiigfany one external transitionA frequency iixes sLlC, and there-- by fixes.' alli of the` remainingexternal'transition frequencies; fixing any two transition frequencies of which at least one is an interna-l transition frequency fixes S-2LIC1 and )YESLl/L/ andthereby fixes a'll'V of the remaining transition. frequencies-external; and internal.

rEhe relative widths of allv of the bands.

(transmitting` bands and attenuating bands) depend onY only one parameter-namely, the ratio ESLl/L". Thus, fixing' ESLl/L,

.fixes the relative widths of allthe bands..

Fixing theratio ofthe widthsv of any two bands not both of which are compound bands iixes and therebylixes the relative widths of all the bands.

In' Fig.Y 3 the transmitting bands are represented as being relatively narrow7 compared with the` attenuating. band-s. vWith existingloadedV lines this is indeed the case, t

but it is not an inherent relation: for any number of the transmitting bands can. be

made wider than the associated attenuating Such applications of the formulas, will., now'be illustrated, after sum-v Y internal transitionE frequency f depends on. two; independent.

bands by so designing the loading (lumped or smooth or both) to secure a sutliciently large value ot the ratio ).ESLl/L/ (llonfevern :tor any lined loading, there is some 'trequency beyond which the transmitting bands are narrower than the associated attenuating bands.)

l1 o illustrate the tiret-mentioned object oit my invention, suppose there is given a loaded line of specified constants and that it is desired to provide appropriate signaling apparatus in combination with this line to enable the minor transmitting bandswin addition to the major transmitting bandto be utilized as transmitting channels for signaling purposes. The tundamental step is to determine the locations and Widths of the transmitting bands, and this can be accomplished by means of the formulas and curves already furnished in this specification.

As a .first illustrative example l have chosen a very lightly loaded open-Wire line having the following values ot capacity, induc'tanee, and loading coil spacing:

ClztllXlO-G tarad per mile.

li,:.00367 henry per mile,

,ll/:.6578 henry,

a :15.76 miles,

ESLl/L/ The following table shows the locations and Widths ot the lirst eight transmitting bands of this loaded line.

| fx1-f- (fn-fn- Dn. fix-hn fn. mb bro/f1. .8G04 l 0 3,140 3,]/l0 1,000 2. 0237 l 732 7, 403 l, G71 532 ri. 4256 11,464 l2, 50i) 1,035 .330 Ll. m32 l i7, 196 17. Q29 733 234 (i. i373 l 22, 923 23, 490 562 lT 7. 9787 y 2S, 6E() 29, l115 l155 l-"I 9. 529/1 i /l, 392 34, 771 382 122 l1. 0856 10,l2-l 40, 452 328 105 This table was computed by means ot torrnulas (3), (l2), (ll Y), (lo) bollore the general curves in Fig. Ll had been constructed. llllith lig. l available, such tables can be constructed With relatively little labor.

'F he numbers in the first column ot the foregoing table are merely the designation numbers ot' the lirst eight compound bands. lt will be recalled that a compound band consists ot a transmitting band and the immediately succeeding attenuating band; for instance, the lirst compound band (71:1) consists oli the .first or major transmitting band and the Jliist attenuating band-immediately `lfollowing. The numbers in the columns headed. f and fn are the transition l'i uuencies constituting respectively the loi* nd the upper boundary points oit the tr:;u.;uiitting hands; and the numbers in the column headed fn-f are therefore the Widths of the transmitting bands. The last column represents the relative Widths of the transmitting bands7 referred to the first or major transmitting band- Whose Width is f1-O:fl.

F ig. gives a graph of the attenuation constant A (per periodic interval) o'l this loaded line as a function ot the frequency, 'for the limiting case of no dissipation; it thereby depicts not only the locations and Widths ot' the transmitting bands (AIO), but also the magnitude ot the attenuation in the attenuating bands, and thus furnishes a basis of information for providing appropriate signaling apparatus in combination With the given loaded line for utilizing its various transmitting bands. This graph Was computed by means of equation (26). T he effect (not shown) of dissipation in the loaded line is, ofcourse, to introduce some attenuation into the transmitting bands-an ellect Well-known as regards t-he first or major transmitting band. A detailed numerical study made by me, by means ot the general formula (22) tor the propagation constant lzA-l-fB,

has shown that the attenuation in the sncceeding transmitting bands increases progressively. ln practical applications this fact might render desirable the employment o't correspondingly more powerful ampliliers in the .succeeding transmitting bands, or even the employment ot' attenuation equalizers.

Before leaving this illustrative example, it may be remarked that the above tabulated values ot Tn and D, are not restricted to this particular loaded line but pertain to any loaded line having equal to unitysince n, and Dn depend only on a. Likewise the graphed values ot A, when plotted as a. :tunetion ot l) instead of pertain to any loaded line having )tzl-since by (26), ll depends only on D and a. By (2), D is directly proportional to y". ln particular, the tabulated values Would hold for a cable having the same constants per periodic interval as the contemplated loaded open-Wire line; that is, ttor a cable having a combination olI lumped and smooth loading as follows:

ljz. 578 henryzinductance ot each loading coil,

L:.O57S henryzinductance of each linesegment between loading coils,

Cz'llXlO-G taradszcapacity of each line-segment between loading coils.

lt C1:.O62 lO-G ta-rads per mile, which is r A. nesentat'ive of its value in actual cables, then the loading coil spacing would be SIC/122.12 miles.

lai-lense .lnrlL/sm henry per mile; and

lGO

" thusjthe smooth loading j( obtaine'dtby means LIOQll "henry, s :7:88 fmiles.

Cl and VL1-'have the same valuesas'in 'the first 'illustrative example; but now )t:012.

The 'following table corresponds to that of the 'first .examplefexcept that it has Snot j'been'car'ried farther than the 'fifth band.

'Comparison of this table with the Liirst shows the greatfdiversity between the tWo illustrative examples: The minor transmitvtingban'ds 'of 'the secondexainple are muc/h narrower -located at much 'higher frel-quencies than in the -first 'e'isainple 'It 'will be recalled that Ethe"second-inen- Vtioned object of my invention Ais to provide a loaded Eline having transmitting bands `of any desired locations and avidthsnot incompatible With the inherent relations, al- ;ready set for'th. 1t will `be 'remembered that the. 'inherentrelations are such lthat only two 'transition frequenciesrmay vbe arbitrarily specified, and that 'aft 'least one Vott' 'these vmust 'be the upper 'boundary Afire'- quency of al transmitting' band. Because of its l.practical importancait would usually 4lie desired to speciiythe value of fthe crit-ical frequency f1; fcoinpa'tibly with this, Vr'there could be specified the loiver boundary frequencyfn 1,`of the nth transmitting band, for any chosen value of n. Also, vit would usually be .desirable'for the nominal iin'- 'pedance 7c to have a particu-lar value; 7c being delined by the equation i: ,T aLlJfLq so. 4 loa) However, not every practical case `presents enough undeteriniiied constants or parameters to admit of imposing asma'ny as three'conditions; for instance, in cases C and D bellow, .only tivo conditions lcan be imposed. f

rlhe lequations funduame'nta'l` for 'designpurposes are (19), (17), (5), (1), (8); of which (17) vand (8) are particular forms of (16) and (7) resp?'ectivelynV Because of frequent luse bellow for designpurposes, it may herab@ madam (it) aivi'deaiby (5) gives This and (8) together determine A; that is, 70

For purposes of illustratingthe vsecondmentioned object oi my invention, have 1,5

gives K L^= meuk/warnen 1 +u (1A) is unownfrom (2-1) 'riienaiilfian' gives oi-nk `w runny, from (5) and (2112);

sC1- -2 kfn 1y/ .I (3A) 4 It is seen from (QA) 'and (3A) that 'the Ydata Yand requirements of Athis Acase vdo not determiney Cl, L1, and s individually; but, as might beV expected, only SL, and SG1-e namely the total inductance and totalY cafpacity o'l eac'h line-segment Abetween loading coils. Thus any one of vthequantities CH fLl, s is free to be specified. lnmany ,practifca'l instances, s would befiiiied; then L, and 'C1 Would be determined forthwith by (2A) and (8A) respectively. In certain other instances, 'C1 would lb'e fixed; -then s would lbe determined (3A), and thereafter L1 by` (2A). Similarly when Llis fixed,

It Will be recalled that L, represents the smoothly distributed requisite total inductance'per unit length. If L1, denotes 'the natural distributed lin'du'ctance per unit length, then-the amount oft artificial smooth loading tov be applied (by means of per# malloy, for instance) will he lil- L11 per unit length'. y

'Oase 'BQ-'C1 given; L1, L and s free; f1, fr 1 and lc specified. This is the case of any given smooth line, (though more particularly a cable) having a given capacity C1, to be so loaded (with lumped loading and also smooth loading) as to have specified values off1,fn n, and 7c. The design problem is to' determine the requisite values 'of L1, L', and s in terms of f1, fpm,

The -solution =can ibe ico (Sil

Next.i and (1B) )t is known from give L1: clica/(i +A). (2B) Then lizslil/t gives, by means of (1B) and (2l-3);

with )t known from (21).

lil represents the smoothly distributed requisite total inductance per unit length. lt lin denotes the amount of distributed inductance per unit length possessed by the line originally, then the amount ot smooth loading' to be applied (by means of permalloy, for instance) will be lil-Lu per unit length.

(Msc 0,-01 and L1 given, L flandfblyu specilied.

This is the case of an existing smooth line (C1, Ll-ol" which L1 may consist partly ot smooth loading) to be so loaded with lumped loading as to have specihed values ot f1 andfbm. rlhe design-problem is to determine the requisite values tor L and s in terms ol 0 L1,f1, and fpm. The solution can be obtained as follows:

Equation gives immediately Substituting this value ot S into (1) gives and s tree;

SzDl/ll'flW/LlCl. Finally, from LzeLI/ and (2D) and oni,

rlhus the final design-formulas are and (3D), with A known from (1B) and hence D1 known from (11) or (12).

Dcr/cations of formulas.

l will now furnish proofs o'lE the abovestated facts and 'Formulas pertaining; to the locations ot the minor t-ransn'iitting bands i (and the associated attenuating,` bands) ot a loaded line some or all of whose loading is periodic or lumped. For this purpose l will start with the formula given though in somewhat diil'erent notation by Campbell (Phil. Mag., March, 1903) for the propagan tion constant rzilia'n per periodic interval of the loaded line, A. and B denoting respectively the attenuation constant and the phase constant (wavelength constant) g the aforesaid `formula :tor F is cosh 1`=cosh 7 l-g sinh y. (22) Z) denotes the impedance of each loading coil; g and y pertain to each segment oit smooth line between loading coils, g denoting the characteristic impedance, and y the propagation constant; that is where ll and L denote the resistance and inductance olf each loading;` coil, and R1, Gl, L1, C1 the resistance, leakance, inductance, capacity, per unit length, oi' the line segments between loading coils; and z' denotes the imaginary operator already explained, the frequencies that may properly be regarded the boundary :frequencies ot the transmitting bands are the boundary frequencies ot the transslitting;` bands oit the corresponding non-dissipative loaded line-that is, ot' the loaded line for which lt', R1, and G1 are zero7 so that Y The general formula (22) for the propagation constant Il of the loaded line then reduces to cosh I`=cos 2D -lg sin 2D, (26) by aid of (1) and yl`his formula (25) can be transformed to the following', which will be found more coi'ivenient tor certain 'purposes s It should new be noted, ,from A(26) and (27), that cosh F and sinh2 'F are both pure real for Aa non-dissipative loaded line.

vThe locations ofthe -transniitting bands will now be found by making a study of cosh I cosh (A -l-t'B) cosh A cos B +r; sinh A sin B.

,cosh A cos B =cosh T, (31) When cosh2 I 1, ,that Eis, sinh2 1` 0 then A: O: and B =cos*1 cosh I;

equations (26) and (27) so as to determine the D-ranges of no .attenuation (A20).

lVhen .cosh Iv is lniown, .the components A and B of F can loe evaluated by means of the identity with, of course, the added restriction that A .must be real and positive, and B real.

From (30) and (31) it follows that when cosh2 I` l, tha-t is, sinh2 I 0f, then A=coshd1 I cosh I l and B=gar; (33') cosh F being' real, and g being` an even or an kodd integer aecordingas cosh F is .positive or negative respectively. From (32) and (33) it is seen that the transmitting bands (AzQ) are characterized Yby :the inequality sinh2 -I` 0 and the attenua-ting bands (A/O) by the inequality sinh2 I" ,O,.and hence that the transition points between ,these two kinds of bands are characterized by the equation sinh2 FIO.

The transition values of D are the zeros (roots) of the first three factors of the equation (27) .for sinh2 F. The zerosof .the factor sin2 2D are at Dram/2, with m20, 1, 2, 3, l; thus they subdivide the D-scale into segments of Width 1r/2 each, as represented byV Fi. 3. The Zyeros of Athe factors D tan 'D-)t'and D cot D-I-)t are situated in the odd and even numbered segments respectively because A, as defined by (1), 'is essentially positive; there is only one zero in each segment.

Formulated analytically, with the .arguments ofthe trigonometric functions reduced `to the smallest positive values that preserve the values of 'the functions, Ithe transition values of D are the :values of DWH and Dm satisfying the vecpuations S1112 2(1)rlln+l :0, (34) 13 'tan D'-{a-1]g)=i, (35) with. 774:0 la 21.3.5 in 7f3/21023 3, in (35). Equation (34) is equivalent to W )Vith n odd and with n even, (35) .is equivalent respectively .to

D 13ml D-IO By .inspection of (27) it can be verified that sinh2 F is negative When Dnflm D D11 and positive when D D Dn,n+1;

The values of Dn, namely the roots of (35), cannot be Written down directly nor' eXpressed exactly But :they can be found to any desired degree of approximation by hrst developing the` left side o f into a power series involving Dn; and then, by successive approximation 0r by undetermined coeiiicicnts, solving. the .resulting equation so as to express Dn as a power kseries in ),t-that is, reverting the first series to obtain .the second. It was in this Way that I :obtained formulas (1,0) and (11),. (Rever.sion off series by the method of undetermined coeficients is treated in most advanced algebras and in books ontlietheory lof infinite series.) When a more convergentpower seriesv Vthan (10) is needed it can be Vobtained by expanding the original functipn inV `the neighborhood of a value of the variable known to be an .approximate solution of the equation to be solved, and then reverting. the resulting series. However, the formula (12) ofsuccessive approximation; meets all the needs 0f numerical evaluation of Dn, for all the values of a--including` 71:1. n

The formula (12) of successive approximation @an be derived from by application of' Newt'ons method,A which may be Looe formulated in general as follows, m denoting1 the unknown quantity to be evaluated: Let the equation to be solved for x be Written in the form Let WL denote a known approximate value ot ai, and /tl the unknown butsinall ditference between the unknown exact value of a? and the approximate value w1, so that crawl-Hal.

Then an approxiu'iate value tor theI small correction term /Ll can be obtained by application or" Taylorls theorem:

wherein qtal), (fcl}, are the tirst, Second, derivatives et {Mtr} with respect to 00, evaluated at mzl. When the teru'is containing higher powers oilI 7L. than tl t't *l1 l t^l 'Y il ie 11st power ale negectet, equation (eo) yields the following` approximation tor 72,3.

This approximate value for 7L, nf'hen added to the tiret approfiin'iation Q21 for m yields a second approximation for namelv @Sima-blt2) :O corresponding' to equation (36) with and h2 corresponding to m1 and tl respectively. ln the present application ot Newtons method, to the derivation ot (12) from 35),

l Will non7 briefiy describe several graphical methods which are useful not only for determining approximate values ot the internal transition frequencies, but also for verifying; readily many of the facts proved analytically' above.

For the sake oit brevity, the graphical methods to be de'scii'ibed Will be torinulated explicitly with reference to the transition values ot D instead ot the frequency f; but, by the two are related by the simple equation D :afee/L10; the transition values of f thus being obtain- 'able by dividing the transition values of D by 7F31/.l1C1 n "he various graphical methods for mining` Dl1 correspond to the various Ways oit writing tne itunction (D tan D-A.) (D cot D-l-) Whose reros are the values oit Dn.

To formulate the 2graphical methods concisely, let E denote any Yfunction ot the variable D, so that, geeinetrically E is the ordinate corresponding to the abscissa D. of thev various possible graphical methods are then briey but completely indicated by the following` respective statements that the internal transition points Dn are the abscissas ot' the points of intersection ot:

l. The horizontal straight line EIA with 'he curves EID tan D 5 the horizontal straight line Ez-A with the curves lzD cot- D.

2. The straight line EID with the curves EIA cot D;

the straight line Er-D with the curves EIA tan D.

3. 'llhe straight line EzD/)t with the cotangent curves Ezcot D; the straight line E:-D//\ with the tan` gent curves 10() Eztan D.

d. The hyperbola EIA/D with the tangent curves Eztan D; the hyperbola E:-/\/D With the cotangent curves Ezcct D.

5. The parabola E:D2//\-,\ with the curves EzQD cot 2D.

6. The curve EzD/Q-A/QD, compound-- ed ot the straight line and the hyperbola Ezel/en,

llt)

With the cotangent curves nizcot 2D. Methods l, 3 4 'follow from the lormula for sinhL Il when Written in the form (27) or forms obtainable directly therefrom; methods 5, 6 follow from (28).

Some or all of these graphical methods show clearly that one and only one transition value of D lies u'ithin cach of the segments of width 7r/2;

the zeros of /\-D tan D and of )t-l-D cot D are situated in the odd and eren numbered segments respectively; with increasing' D, the transmitting banns continuallyY decrease in width and the attenuatingbands continually increase in Width, the change taking place rapidly at lirst and then more and n'iere s-nlowly, increasing )t increases the ratio of transmitting band Width to attenuating band Width.

it will be obvious that the general principles herein disclosed may he embodied in many other organizationsWidely diiferent from those illustrated Without departing from the spirit of the invention as defined in the following claims.

What is claimed is:

1. A transmission line having distributed capacity, distributes inductance and lumped inductance, said capacity, distributed inductance and lumped inductance having such relative values with respect to each other as to produce a major band of free transmission extending from zero to a preassigned upper cut-oft frequency, and said distributed and lumped in'ductances being so proportioned to each other to produce a plurality of minor bands of free transmission at successive intervals above said major band andihaving frequencies low enough to permit of signal transmission Without undue attenuation.

2. A transmission line having distributed capacity, distributed inductance and lumped inductance, said capacity, distrib-uted inductance and lumped inductance having such relative values with respect to each other as to produce a major band of free transmission extending from Zero to an upper cutoff frequency, and said distributed and lumped inductances being so proportioned to each other as to produce a plurality of minor bands of free transmission located at successive intervals above said major band and having frequencies low enough to permit of signal transmission Without undue attenuation, said bands being separated from each other by attenuating bands.

3. A transmission line having distributed capacity, distributed inductance and lumped inductance, said capacity, distributed inductance and lumped inductance having such relative values with respect to each other as to produce a major band of free transmission extending from zero to a'preassigned upper cut-olf frequency, and said distributed and lumped inductances being so proportioned to each other as to produce a plurality of minor bands of free transn'iission at successive intervals above said major band and having frequencies low enough to permit of signal transmission Without undue attenuation, each of said minor bands being of lesser' Width than the major band.

4i. A transmission line having distributed capacity, distributed inductance and lumped inductance, said capacity, distributed inductance and lumped inductance having such relative values with respect to each other as to produce a major band of free transmission extending from zero to a preassigned upper cut-off frequency, and said distributed and lumped inductances being so proportioned to each other as to produce a plurality of minor bands of free transmission at successive intervals above said major band and having frequencies loW enough to permit of signal transmission Without undue attenuation, each of said minor bands being narrower than the major band and each minor band being narrower than the next band below it in the frequency spectrum.

5. A transmission line having distributed capacity, distributed inductance and lumped inductance, said capacity, distributed inductance and lumped inductance having such relative values Wit-h respect to each other, said distributed and lumped inductances being so proportioned to each other as to produce a plurality of adjacent compound bands of equal Width, each compound band comprising a band of free transmission and the succeeding attenuating band, said bands of free'transmission having frequencies low enough to permit of signal transmission Without undue attenuation.

6. A transmission line having distributed capacity, distributed inductance and lumped inductance, said capacit-y, distributed inductance and lumped inductance having such relative values With respect to each other, said distributed and lumped inductances being so proportioned to each other as to produce a plurality of adjacent compound bands of equal Width, each compound'band comprising a band' of free transmission and the succeeding attenuating band, said bands of free transmission having frequencies low enough to permit of signal transmission Without undue attenuation, the band of free transmission of each compound band being narrower than the corresponding band of free transmission in the compound band just immediately below it in the frequency spectrum.

7. A transmission line having distributed capacity, distributed inductance and lumped inductance, said capacity, distributed inductance and lumped inductance having such relative values With respect to each other, said distributed and lumped inductances being so proportion-ed to each other as to produce a plurality of transmitting bands separated by attenuating bands, said bands of free transmission having frequencies lon7 enough to permit of signal transmission Without undue attenuation, the lower limiting frequencies of the free transmission bands being` equally spaced, and the ratio of `the transmitting band Width to attenuating band Width increasing as the ri tio of the distributed inductance to the lumped inductance increases.

8. ln combination with a transmission line havingl a major band of free transmission and plurality of minor 'transmitting bands of lesser Width successively located above said major band. a main signaling channel comprising apparatus for transmitting and receiving signals over said major bano, and a plurality of carrier channels each comprising carrier transmittingV and r rrier receiving` apparatus having carrier r cies as signed thereto falling within oef 4ain of said minor bands of free transmission.

9. In combination With a transmission line having a major band of free transmission and a plurality of minor bands of lesser Width successively located above said major band, a main signaling channel comprising telephone transmitting and receiving apparatus for transmitting voice frequencies Within said major band of free transmission, and a plurality of carrier channels each comprising carrier transmitting and receiving apparatus, said carrier channels having assigned thereto carrier frequencies falling Within certain of said minor bands of free transmission.

l0. In combination with a transmission line having a major band of free transmis sion and a plurality of minor bands of lesser Width successively located above said major band, a main signaling channel comprising apparatus for transmitting and receiving signals over said major band, a plurality of carrier channels each comprising carrier transmitting and carrier receiving apparatus having carrier frequencies assigned thereto falling within ce 'tain of said minor bands of free transmission, and selective means associated With each channel selective of frequencies corresponding to the band of free transn'iission utilized by the channel.

ll. ln combination with a transmission line having a major band of free transmission and a plurality of minor bands of lesser Width successively located above said major banrh a main signaling' channel comprising telephone transmitting` and receiving apparatus for transmitting voice frequencies Within said maj or band of free t ansmission a plurality of carrier channels each comprising carrier transmitting and receiving apparatus7 said carrier channels having assigned thereto carrier frequencies falling Within certain of said minor bands of free transn'iission9 and selective means associated With each channel selective of frequencies corresponding to the band of free t ansmis sion utilized by the channel.

ln testimony whereof, ll have signed my name to this specification this 8th day of July 1924.

RAY S. HOYT. 

